
Discretuum. \(V(z)\rightarrow \infty \)  as \(z\rightarrow \infty \) . This is the case when there exists an IR brane, as in RS1 models [1]}, or for certain soft-wall models in which the warp factor decays fast \(A(z)\propto z^{\alpha },\alpha >1\) . The singularity in the IR, a brane or a soft-wall, signals the breaking of the CFT in the IR. It is a hard breaking, the theory confines and we get the KK modes, the composites of the broken CFT. The mass splitting goes roughly as \(\Delta m_{KK}=\frac{\pi }{z_{IR}}\) , where \(z_{IR}\)  is the position of the brane or the soft-wall.

Continuum without a mass gap. \(V(z)\rightarrow 0\)  as \(z\rightarrow \infty \) . This is the case with the AdS background, dual to an unbroken CFT, as in for example RS2 model [2]}.

Continuum with a mass gap. \(V(z)\rightarrow \mu ^2>0\)  as \(z\rightarrow \infty \) . The dual CFT is softly broken such that the continuum is untouched but starts at a finite threshold, \(\mu \) . This behavior has been studies in a variety of scenarios [3]}, [4]}, [5]}, [6]}

